Re: [Maxima-discuss] Integrating piecewise defined functions

[Eduardo O. <edu...@gm...>]

On Thu, 28 Nov 2024 at 04:51, Jaime Villate <vi...@fe...> wrote:

>
> On 27/11/24 21:56, Eduardo Ochs wrote:
>
> Hi list,
>
> what is the recommended way to integrate piecewise defined
> functions? I tried this,
>
>   f(x) := if     x<0 then 0
>           elseif x<1 then 1
>           else            0;
>   g(x) := if     x<0 then 0
>           elseif x<1 then x
>           else            0;
>   h(x) := integrate(f(t)*g(x-t), t, -2, +2);
>
> and I couldn't find a way to make Maxima calculate this
> integral...
>
> Hello Eduardo,
>
> If you mean the convolution of f and g:
>
>    h(x) := integrate(f(x)*g(x-t), t, 0, x)
>
> I recommend that you use Laplace transforms and expressions, rather than
> "functions":
>
> f: hstep (x) - hstep (x-1);
> g: (hstep (x) - hstep (x-1))*x;
> F: laplace (f,x,s);
> G: laplace (g,x,s);
> H: F*G;
> h: pwilt (H,s,x);
> plot2d ([f,g,h], [x,-2,2], [legend,"f(x)","g(x)","h(x)"]);
>
> Cumprimentos,
>
> Jaime
>

 Hola Jaime!

Thanks! Excellent modulo a bug, that may be between keyboard and chair
or not... I was expecting h(x)=0 for x<=0, and according to the plot
we got h(x)=x^2/2 for x<=0. What is going on?

  Thanks in advance,
    Eduardo (who has used LTs very little =( )